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Kepler’s Laws—20 Jan • Homework 1 • • • • Clicker • • • • Register at iClicker.com Use your email address You may use paper answers 2 times. The discovery of the laws of motion, the first science. • • • • Due at 6:00am on Thurs, 22nd Jan. On angel.msu.edu, go to Lessons>Homework>Homework1. The lower grade does not count. De Revolutionibus Orbium Coelestium, Copernicus, 1543 Astronomia Nova, Kepler, 1609 Philosophiae Naturalis Principia Mathematica, Newton, 1687 How Kepler figured out the path of Mars from Tyco’s observations. Discovery of his three laws. Kepler at 39, Sternwarte Kremsmünster http://members.nextra.at/stewar/ Copernicus 1473–1543 Columbus sails 1492 Tycho Brahe 1546–1601 Shakespeare 1564–1616 Johannes Kepler 1571–1630 Jamestown 1607 King James Bible 1611 Harvard College 1636 Isaac Newton 1642–1727 Questions on reading 1. When Kepler was a college student, the most accurate description of the motion of planets uses the terms a. Velocity, position, & acceleration b. Circular orbits c. Elliptical orbits 2. Same question for Newton 3. Today the most accurate description of the motion of planets uses the terms a. Velocity, position, & acceleration b. Circular orbits c. Elliptical orbits ISP 205-2 S2009 1 Tycho Brahe’s Observations Uraniborg What is fake on Tycho? • On Uraniborg, Tycho measured positions of the planets for 20 years • Highly accurate & reliable Brass azimuthal quadrant, 65 cm radius (ca 1576) • Accuracy limited by human eye, not by instruments. Superseded only with telescopes. • Tyco measured & compensated for instrument flexure, the biggest error. Great quadrant (1582) Kepler analyzes Tycho’s data • Kepler was Tycho’s assistant • 20 yrs’ data on planetary motions. • Tycho tried to fit data with Ptolemy-like model. • Kepler analyzed the data • Found 3-d orbits from 2-d positions in the sky • Concentrated on orbit of Mars. • Had to subtract off Earth’s (imperfectly known) orbit. • Discovered 3 “laws,” which describe the motions of the planets. ISP 205-2 S2009 Brahe (1546-1601) Kepler (1571-1630) • Their meeting at Benatek (in Czechoslovakia) • …on 4 February 1600, Tycho de Brahe and Johannes Keplerus, co-founders of a new universe, met face to face, silver nose to scabby cheek. Tycho was fifty-three, Kepler, twenty-nine. Tycho was an aristocrat, Kepler a plebian. — Koestler, The Sleepwalkers, p302 2 Kepler’s First Law 1605 • Orbit of a planet is an ellipse, with the sun at one focus. • Definition of an ellipse • (Distance between planet & focus #1) + (distance between planet & focus #2) is the same for the entire orbit. • This was an unexpected result in Kepler’s time. • Ellipse is a simply defined shape, not any shape. The motion of the planets must have a deeper cause. • If the sun is at a focus, it must affect the planet’s motion. Semi-major axis Minor axis Sun, at one focus Major axis Kepler1 simulation Semi-major axis Earth’s orbit is nearly circular Kepler’s Second Law 1602 • The line joining the planet and the sun sweeps out equal areas of space in equal amounts of time. • Planet moves • more slowly when it is far from sun • more rapidly when close to sun Kepler2 simulation ISP 205-2 S2009 3 Kepler’s Laws • Law 1: Orbit of a planet is an ellipse, with the sun at one focus. • Law 2: The line joining the planet and the sun sweeps out equal areas of space in equal amounts of time. 2. Winter is a few days shorter than summer for us in the northern hemisphere. Therefore Earth is at A, B, C, or D in January? • What do I need to find out before I can answer the question? A D Minor axis Sun Major axis C B Kepler’s Third Law 1618 • P2 = a3 • P = period of orbit, in years • a = semi-major axis of orbit, in AU. (Average Earth-sun distance is 1 AU.) Fast solar simulation http://web.cuug.ab.ca/~kmcclary/fastsolar.html ISP 205-2 S2009 4 Kepler’s Third Law 1618 • P2 = a3 • • P = period of orbit, in years a = semi-major axis of orbit, in AU. (Average Earth-sun distance is 1 AU.) 1. A 10th object (planet?) was found beyond the orbit of Pluto. has the shorter period. A. Pluto B. 10th object C. Not enough information to answer. • What do I need to find out before I can answer the question? Questions concerning Kepler’s Laws • • • A planet’s path is an ellipse with the sun at one focus. A planet “sweeps” out the same area in an equal amount of time. The planets’ periods P and semi-major axes a are related by P2=a3 ISP 205-2 S2009 • A planet, which has an almost circular orbit, and a comet, which has a highly elliptical orbit, have the same periods. Draw their orbits on a single picture. 1. Grading: sun’s position 2. Grading: lengths of major axes. • What do I need to find out? 5 Questions concerning Kepler’s Laws • • • A planet’s path is an ellipse with the sun at one focus. A planet “sweeps” out the same area in an equal amount of time. The planets’ periods P and semi-major axes a are related by P2=a3 • A planet, which has an almost circular orbit, and a comet, which has a highly elliptical orbit, have the same periods. Draw their orbits on a single picture. 1. Grading: sun’s position A. Centered for comet B. Offset for comet 2. Grading: lengths of major axes. A. Same for both B. Different The Motions of the Planets Ptolemy 140 AD ISP 205-2 S2009 Copernicus 1543 Kepler 1609 Simpler model More accurate description of data 6 Kepler’s 3 Laws • Orbit of a planet is an ellipse, with the sun at one focus. • The straight line joining the planet and the sun sweeps out equal areas of space in equal amounts of time. • P2 = a3 • But why? • These are descriptive laws, but there must be deeper reasons for the planets to do this. Newton’s Laws of Motion & Gravity • • • De Revolutionibus Orbium Coelestium, Copernicus, 1543 Astronomia Nova, Kepler, 1609 Philosophiae Naturalis Principia Mathematica, Newton, 1687 • Newton invented calculus (MTH 132) & mechanics (PHY 183) • Nature and Nature's laws lay hid in night:/ God said, Let Newton be! and all was light. —Newton’s epitaph by Alexander Pope • Newton: Same laws apply to a falling apple & moving planet. • Description of motion • Gravity ∝1/R2 implies K’s 3rd Law ISP 205-2 S2009 Isaac Newton (at 47) by Godfrey Kneller Trustees of the Portsmouth Estate www.huntington.org/LibraryDiv/Newton/Newtonexhibit.htm Copernicus 1473–1543 Columbus sails 1492 Tycho Brahe 1546–1601 Shakespeare 1564–1616 Johannes Kepler 1571–1630 Jamestown 1607 King James Bible 1611 Harvard College 1636 Isaac Newton 1642–1727 George Washington 1732-1799 7